Q=The probability of obtaining a head when a biased coin is tossed is p, where p < .An experiment consists of tossing the coin 20 times and recording the number of heads.In a large number of experiments the variance of the number of heads is found to be 4.2.a Estimate the value of p.b Hence estimate the probability that exactly 7 heads are recorded during a particularexperiment.c)x istis the random variable such that X~ B(15, p) and Var(X) = 2.4.Find the two possible values of p.1

Binomial distribution has two outcome only. One is occurrence of success and another is occurrence…

Answered: The probability of obtaining a head…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Let x be a random variable that represents the pH of CVS brand water. The mean of this x distribution is µ = 6.5 pH. A new company wants to sell its water at CVS locations. However, CVS management believes that the new brand will have a mean pH less than the CVS brand water. A random sample of 50 water samples were taken from this new company's water and it was found that the sample mean was 6.3 pH and the sample standard deviation was s = 0.5 pH. Do the data indicate that the new company's water has a mean pH level less than 6.5, which is the pH of the CVS brand water. Use a 5% significance level. Identify the following in your answer. 1. Identify the null Ho and alternative hypotheses H1 for the problem. 2. Identify the following: Sample statistic • Test Statistic (t): (Round to three decimal places) p - value: (Round to four places) • Calculator key used. 3. Identify the significance level and determine if you reject or fail to reject the null hypothesis. 4. State your conclusion.
Assume that the random variable X is normally distributed with mean = 15 and standard deviation = 2. Let n = 4. Find P( > 16) and P( < 16).
where appropriate. 1. Experience has shown that the seeds from a certain variety of orchid have a 75% chance of germinating when planted under normal conditions. Suppose n seeds are planted, and let X be the random variable that counts the number of seeds that germinate. (a) What type of random variable is X? Indicate both the type and the appropriate parameters using the "~" notation. Write down the pmf of X, and do not forget to indicate the range of values that x can take on. X ~ px (x) = = (b) What is the minimum value of n so that the probability of at least five of the seeds germinating is at least 90%?
Service time for a customer coming through a checkout counter in a retail store is a random variable with the mean of 4.0 minutes and standard deviation of 2.0 minutes. Suppose that the distribution of service time is fairly close to a normal distribution. Suppose there are two counters in a store, n₁ = 46 customers in the first line and n₂ = 52 customers in the second line. Find the probability that the difference between the mean service time for the shorter line X₁ and the mean service time for the longer one X₂ is more than 0.3 minutes. Assume that the service times for each customer can be regarded as independent random variables. Round your answer to two decimal places (e.g. 98.76). P = !
Service time for a customer coming through a checkout counter in a retail store is a random variable with the mean of 3.5 minutes and standard deviation of 3.5 minutes. Suppose that the distribution of service time is fairly close to a normal distribution. Suppose there are two counters in a store, n₁ = 2 customers in the first line and n₂ = 13 customers in the second line. Find the probability that the difference between the mean service time for the shorter line X₁ and the mean service time for the longer one X₂ is more than 0.1 minutes. Assume that the service times for each customer can be regarded as independent random variables. Round your answer to two decimal places (e.g. 98.76). P =
Weights of Lamb after eight weeks after born are normally distributed with mean µ = 14 kg and variance σ 2 = 4. a)Find the probability p that a single lamb has weight less than 12 kg. b) Find the probability that exactly 3 of the next 5 lambs examined will have weights less than 12 kg.
Assume X and Y are independent random variables with X ~ Binomial(n =100, p = 0.2) and Y ~ Pascal(m =16, p = 2/3) . Find the indicated expected value and variance. a. E(3X + 2Y +1) b. Var(3X + 2Y +1)
Assume the flying height of an airplane is a Gaussian Random variable X with ax = 5000 m and ox=2000 m. Find the probability of the airplane flying higher than 10000 m. Use the table method.
Let X be a binomial random variable with a mean of 0.5 and a variance of 0.45. Find P(x is greater than or equal to 1)
Service time for a customer coming through a checkout counter in a retail store is a random variable with the mean of 1.0 minutes and standard deviation of 0.5 minutes. Suppose that the distribution of service time is fairly close to a normal distribution. Suppose there are two counters in a store, n = 11 customers in the first line and n2 = 30 customers in the second line. Find the probability that the difference between the mean service time for the shorter line X1 and the mean service time for the longer one X2 is more than 0.5 minutes. Assume that the service times for each customer can be regarded as independent random variables. Round your answer to two decimal places (e.g. 98.76). P = i
Let the random variable X be normally distributed with mean 6 and variance 4. (A) Find the probabilityP(6.3x )=0.36.
Total blood volume (in mi) per body wight (in ke) is important in medical research. For healthy aduks, the red blood cell volume mean is about p = 28 ml/kg.t Red blood cell vokume that is too lom ar too high can indicate a medical problem. Suppose that koger has had seven blood tests, and the red blood cell volumes weré as follows Let x be a random variable that represents Roger's red blood cll volume. Assume that x has a narmal distributian and - 4.75. Do the data indicate that koger's red blood cell valume is different (either way) from a- 28 mi/kg? Use a 0.01 lervel of significance. a What is the leval of sigaicance State the null and alternate hypotheses. Will you use a left-lailed, right-laded, or two-tailed test? O H: - 28 ml/kg; H: 2s m/kg; Ima-tailed o Ho: - 28 ml/ka; H 28 m/ka, let-tailed O Ho: 28 mil/kg: H1:- 28 ml/kg; tmo-tailed O Ho: 28 m/ka, H > 28 m/kg; right-laiked (b) What sampling distribution wil you use? Explain the rationale for your choice of sampling distributian.…

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